**Abstract:** A computer program has been developed to generate the X-ray diffraction intensity distribution along any particular reciprocal lattice row, plane, or volume, for any arbitrary group of atoms within a crystal. The program, which maps the intensity in crystal reciprocal space in much the same way as a conventional Fourier series program maps the electron density in direct crystal space, has been used to calculate the expected X-ray diffraction line profiles for a number of montmorillonite and mica crystallites of varying thicknesses in the *c** direction.

The program evaluates the function
G(HKL)=
∑
n−1
N
f
n
exp 2ni(H
x
n
+K
y
n
+L
z
n
),
where *G*(*HKL*) is the Fourier transform of an array of *N*-atoms at a particular *H, K, L* coordinate in reciprocal space, *f _{n}* is the scattering factor of the

The apparent *d*-spacings of the various clay mineral models, as given by the line profiles, approach asymptotically the true value as the number of layers increase. For example, the apparent *d*_{001} spacing for a mica of the composition
K
(Fe, Mg)
3
Si
3
Al
10
(OH)
2
is 12.91, 11.35, 10.79, 10.53, 10.38, 10.22, 10.14, 10.04 and 10.02 Å for crystals 2, 3, 4, 5, 6, 8, 10, 20, and 30 layers thick, respectively. For the infinitely thick crystal, *d*_{001}=10.000 Å. The apparent *d*_{001} spacing for a montmorillonite of the composition K_{0·33}Al_{2}(Si, Al)_{4}O_{10}(OH)_{2}·4H_{2}O (true *d*_{001}=15.400 Å) is 18.85, 16.80, 15.87, 15.52, and 15.41 Å for crystals 2, 3, 5, 10, and 30 layers thick, respectively.

These diffraction profiles and line shifts can be used in analyzing montmorillonites, micas, and mixed-layer montmorillonite-mica clays.

*Clays and Clay Minerals*; 1967 v. 15; no. 1; p. 47; DOI: 10.1346/CCMN.1967.0150105

© 1967, The Clay Minerals Society

Clay Minerals Society (www.clays.org)